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MODELINGTHEAEROSOLSINTHEATMOSPHEREOFTITAN By JOANNAELIZABETHTHOMAS-OSIP ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2001 Thisisdedicatedtoallthosewhoencouragedandsupportedmethroughoutthelengthy ordealofgraduateschoolandtothosewhocomeaftermeandhaveneedofthesame. RememberHenryFord'swords"Obstaclesarethosefrightfulthingsyouseewhenyou takeyoureyesoffyourgoal." ACKNOWLEDGMENTS FirstandforemostIwouldliketothankmyhusband,DavidOsip,forknowing whatIneeded,beitquietsupportorsomecombinationofnaggingandbribing. He believedinmewhenIhadstopped. HehasbeenagreatresourcewhenIlethimhelpme andheprovidesdailyinspirationashestrivestobethebestastronomerhecanbeand achievesthatwithflyingcolors. Secondly,Ithankmyadvisor,BoGustafson,forallowingmethetimeandspace tofigurethingsoutonmyown. Iwouldalsoliketothankallmycommitteemembersfor theirinput. IwouldespeciallyliketothankLudmillaKolokolovawhowasalways willingtodiscussmyworkandmademanyhelpfulcommentsandsuggestions. Shewas alsooftenreadywithanencouragingwordwhenIcametoherforadvice. Iwouldalso liketothankYu-LinXuformanyhelpfuldiscussionsregardingtheoreticallight scatteringandradiativetransfer. Inaddition,heprovidedmewithveryuseful calculationsfromhiscodeforlightscatteringbyaggregatesofspheres. Iwouldalsoliketothankallmyparentsforencouragingmetopursuemydreams eachinhisorherownway. Myfather,JohnR.Thomas,hasgonebacktograduate schoolandmadeitaracetoseewhocouldgetaPh.D.first. Mystep-fatherkeptme laughing. Mymotherlovedmeandremindedmeofthisbytellingme,"Youknow Joanna,itdoesn'thavetobeperfect." in Furthermore,Iwanttothankallmyfriendsfortheirloveandsupport. Fellow graduatestudent,JoannaLevineallowedmetostaywithherandactedasmychauffeur duringmyvisitsbacktoGainesvilleafterwehadmovedaway. Shealwaysmade returningtoGainesvillefunandhelpedimprovemyconfidencebytellingmeIinspired her. Kirk,Nicole,andAnthonyBeckerinvitedmeintotheirhome,sometimes unannounced,andprovidedmeanescapefromtheuniversitywhenIneededit. Tim SpahrlistenedtomeventtoomanytimestocountandsharedmanyatriptoBeezer's whenIneededfries. Fellowgraduatestudent,researchgroupmember,andprevious officemate,ThomasWaldemarssonaskedgoodquestionsandshowedgenuineinterestin mywork. LastlyIwouldliketothankJimElliotforbecomingmysurrogatementorafterwe movedtoBoston. Heprovidedmewithsomegoodadviceandthenecessary encouragement(inthewayofemployment)forfinishingthisdissertation,aswellas somespacetoworkandaccesstoafastcomputeronwhichtorunmymodels. IV TABLEOFCONTENTS page ACKNOWLEDGMENTS i" TABLEOFCONTENTS v LISTOFTABLES v» LISTOFFIGURES viii ABSTRACT xii INTRODUCTION 1 SphericalParticleParadox i 5 HowCanAnalogLightScatteringHelp? 9 SINGLESCATTERINGPROPERTIESOFMODELS 13 ElectromagneticRadiationandPolarization 13 StokesVectors 17 ScatteringbyaSingleParticleandaCloudofParticles 18 ScatteringMatrix 18 Scattering,Absorption,andExtinctionCross-SectionsandEfficiencies 23 ScatteringCalculations 25 RayleighScattering 25 MieTheory-Spheres 26 ExactMultisphereScatteringTheory 27 DiscreteDipoleApproximation 27 EffectiveMediumTheory 28 LaboratoryModelsandtheRationaleBehindThem 29 Cubes 29 Aggregates 31 SingleScatteringMeasurements 39 Procedures 39 DataReduction 41 Averagingoverorientation 41 Calibration 43 Scatteringmatrixasafunctionofscatteringangle 44 Colorandpolarimetriccolor 46 Porosity 48 SingleScatteringResultsfromtheLaboratoryandTheory 49 1 ScatteringMatricesforCubes 52 ScatteringMatricesforAggregates 56 SingleScatteringandTitan 68 POLARIZEDRADIATIVETRANSFERMODELING 76 BasicDefinitionsandRadiometricQuantities 77 AModelAppropriateforTitan 80 TheVectorTransferEquation 81 ThePhaseMatrix 83 FourierSeriesAnalysisinAzimuthAngle 85 Expansionofthescatteringmatrix 87 DoublingandAddingMethod 88 ReflectionandTransmissionMatrices 89 Initialization 94 ReflectionFromASurfaceAtTheBottomOfTheAtmosphere 96 Implementation 96 IntegrationOveraPlanetaryDisk 98 TestingandSensitivityStudies 106 TestingRt3 106 TestingDiskIntegration 11 ParameterSensitivityTests 114 SurfaceandSemi-InfiniteAtmosphereTests 117 SizeDistributionTest , 119 MODELCALCULATIONSOFTITAN'SATMOSPHERE 122 OverviewofEntireModelingProcedure 122 Observations 124 SingleLayerModelResults 126 MoreComplicatedModels 144 PossibleApplicationstoCassini 154 Conclusions 156 FutureWork 159 SingleScatteringIssues 160 OtherTypesofModelstoConsider 161 APPENDIXA RADIUSOFGYRATION 162 APPENDIXB EXPANSIONOFTHESCATTERINGMATRIX 165 ComparisonofLegendrePolynomialstoLaboratoryData 165 ComparisonofLegendrePolynomialstoSmoothedLaboratoryData 172 APPENDIXC INCLUSIONOFTHEFULLSCATTERINGMATRIXIN RADIATIVETRANSFERCALCULATIONS 180 LISTOFREFERENCES 183 BIOGRAPHICALSKETCH 191 VI LISTOFTABLES Table Pa§e 1.1 IndicesofrefractionforTholinandTholinice 8 2.1 Physicalcharacteristicsofcubetargets 30 2.2Physicalcharacteristicsofaggregatetargets 32 2.3 Multi-sphereaggregatecharacteristics 38 2.4 Listofmicrowaveanaloglaboratorymeasurements 40 2.5 Summaryofsomesinglescatteringresults 50 2.6 PhotopolarimetrybestfitH-Gfunctionparameters 69 42..17 RSisnsgvlaelusecsatftoerrianlgltaalrbgeedtosestimatesforallthelaboratorytargets 17244 4.2 ObservedGeometricalbedoofTitanatthephotopolarimetrywavelengths 125 4.3 Geometricalbedoscomputedforsinglelayermodelatmospheres 132 4.4Geometricalbedosforcomputedduallayermodelatmospheres 145 4.5 Geometricalbedosforselectedsinglelayercombinationmodels 147 4.6 SummaryofselectedmodelresultsandTitan'sobservedcharacteristics 157 vn A A 1 LISTOFFIGURES Figure Pa8e 1.1 Pioneer11andVoyager2polarimetryasafunctionofphaseangle 6 1.2 DiagramofmicrowaveanaloglaboratoryfacilityattheUniversityofFlorida 10 2.1 Propagationofanelectromagneticwaveanddepictionoflinearpolarization 15 2.2Thepolarizationellipse 16 2.3 Reciprocalorientation 21 2.4 Mirrorandmirrorreciprocalorientations 23 2.5Photographofthefouracryliccubes 31 2.6 PhotographoftheLSAonaStyrofoamsupport 33 2.7 PhotographoftheBSAonaStyrofoamsupport 34 2.8 PhotographoftheCYAonaStyrofoamsupport 35 2.9 PhotographoftheOA 36 2.10 PhotographoftheS 37 2.1 PhotographoftheCA 37 2.12 RepresentationofXl-4aggregate 38 2.13 Designationoforientationsforacube 42 2.14 Singleorientationintensitymeasurementsforfourdifferentsizecubes 43 2.15 Surfaceplotofintensityasafunctionofscatteringangleandfrequency 45 2.16 Surfaceplotofpolarizationasafunctionofscatteringangleandfrequency 46 2.17 AngulardistributionoftheF-matrixelementsforthe1.5"cube 54 2.18AngulardistributionoftheF-matrixelementsforthe0.5"cube 55 2.19DDAcalculationsandmicrowavelaboratorydatafor0.5"cube 56 2.20AngulardistributionoftheF-matrixelementsfortheLSA 60 2.21AngulardistributionoftheF-matrixelementsfortheCYA 61 2.22AngulardistributionoftheF-matrixelementsfortheBSA 62 2.23 AngulardistributionoftheF-matrixelementsfortheSA 63 2.24 AngulardistributionoftheF-matrixelementsfortheOA 64 2.25 AngulardistributionoftheF-matrixelementsfortheC 65 2.26AngulardistributionoftheF-matrixelementsforaggregatesX1-X4 66 2.27 AngulardistributionoftheF-matrixelementsfortheXI-X4constituents 67 2.28 SyntheticphasefunctionandpolarizationfittingTitanphotopolarimetry 71 4.1 Flowchartofentiremodelingprocess 123 4.2 0.5"cubemodelcomparedtoPioneer11andVoyager2photopolarimetry 133 4.3 1.5"cubemodelcomparedtoPioneer11andVoyager2photopolarimetry 134 4.4 OAmodelcomparedtoPioneer11andVoyager2photopolarimetry 135 4.5 CYAmodelcomparedtoPioneer11andVoyager2photopolarimetry 136 4.6 SAmodelcomparedtoPioneer11andVoyager2photopolarimetry 137 4.7 CAmodelcomparedtoPioneer11andVoyager2photopolarimetry 138 vin 1 4.8 LSAmodelcomparedtoPioneer11andVoyager2photopolarimetry 139 4.9 LSAbluemodelcomparedtoPioneer11andVoyager2photopolarimetry 140 4.10LSAredmodelcomparedtoPioneer11andVoyager2photopolarimetry 141 4.1 X1-X4modelscomparedtoPioneer11andVoyager2photopolarimetry 142 4.12 SingleconstituentspheresfromtheX1-X4aggregatesandphotopolarimetry 143 4.13 LSAandX2combinationmodelcomparedtophotopolarimetry 149 4.14AnotherLSAandX2combinationmodelcomparedtophotopolarimetry 150 4.15 SinglelayercombinationofLSAredandX3comparedtophotopolarimetry 151 4.16SinglelayercombinationofLSAblueandX2comparedtophotopolarimetry 152 4.17 Bestfitmodelatmospherecontaining60%X2/3constituentsand40%LSA 153 4.18 DISRpredictionbasedon60/40combinationmodelat500nm 155 B.l ScatteringmatrixelementsfortheCYAandtheLegendreSeriesfits 166 B.2ScatteringmatrixelementsfortheLSAandtheLegendreSeriesfits 167 B.3ScatteringmatrixelementsfortheCAandtheLegendreSeriesfits 168 B.4ScatteringmatrixelementsfortheXIandtheLegendreSeriesfits 169 B.5 Scatteringmatrixelementsforthe60/40mixofX2constituentsandLSAblueand theLegendreSeriesfits 170 B.6Scatteringmatrixelementsforthe60/40mixofX3constituentsandLSAredandthe LegendreSeriesfits 171 B.7ExampleofLegendreseriesfitfortheunsmoothedLSAdatainbluewaveband....173 B.8ScatteringmatrixelementsforthesmoothedLSAdatainbluewaveband 174 B.9ScatteringmatrixelementsforthesmoothedLSAdatainredwaveband 175 B.10Scatteringmatrixelementsforthesmoothed0.5"cubedata 176 BB..l121SSccaatttteerriinnggmmaattrriixxeelleemmeennttssffoorrtthheessmmooootthheeddO1.A5"dcautbaedata 117787 B.13ScatteringmatrixelementsforthesmoothedSAdata 179 IX AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy MODELINGTHEAEROSOLSINTHEATMOSPHEREOFTITAN By JoannaElizabethThomas-Osip May2001 Chairman:BoA.S.Gustafson MajorDepartment:Astronomy Acombinationoflaboratoryexperiments,theoreticalmodeling,andspacecraftin situobservationsisemployedtocharacterizetheaerosolsintheatmosphereofTitan.The scatteringpropertiesofmodelaerosolsweremeasuredusingtheMicrowaveAnalog LightScatteringFacilityattheUniversityofFloridaandcomplementedwiththeoretical modelingofsinglescatteringcharacteristicsandradiativetransferinTitan'satmosphere. Thisstudycomparesthesemodelingresultswithphotopolarimetricobservationsmade overarangeofphaseanglesbythePioneer11andVoyagers1and2spacecraft approximately20yearsago. Importantresultsofthisworkincludeasurveyofthescatteringpropertiesof differentparticleshapesnecessarytoaccuratelyinterprettheseobservationswithout introducingnon-physicalassumptionsabouttheparticlesorrequiringadditionalfree parameterstotheradiativetransfermodels. Previousstudiesusecalculationmethods